Kinetic processes of muonium formation by thermalized electrons in the spur model

Abstract

Diffusion of a thermalized electron in the field of a Coulomb centre is considered. The time dependence of the probability for the electron not to be captured by the Coulomb centre (μ ⁺) at the momentt,P _D (t), is obtained. The quantityP _D (t) coincides with the precession amplitude at the muon frequency and is determined by the parameterΔ/l _CT (Δ is an averaged distance from an electron to a muon att=0 andl _CT =e ²/(2T) is the Onsager length) that reflects the relation between electron potential and kinetic energies at t=0. WhenΔ/l _CT −1 the precession amplitudeP _D (t) decreases up to 30% during the timel ² _CT /D-(D-is the diffusion coefficient) and then it becomes almost constant. The dependence ofP _D (∞) onΔ/l _CT is presented.